Multiplying Texture Coordinate
Take a look at the cubes below and their materials.



Material of the left cube:



Material of the middle cube:



Material of the right cube:



All three materials above are equivalent, despite using different nodes

What you are doing is multiplying the 3 individual values of a vector (the object coordinates) with a certain value. The second material above might be what you expected what you were supposed to use. It takes a vector, splits it up into individual values, multiplies the values with a number and combines the values back into a vector. If you compare the first and the second material, you can see that they are almost the same, except that the first uses 'color' nodes and the second uses 'vector' nodes. The reason why this gives the same result is because vectors and colors are actually pretty similar. Both consist out of three values ('X','Y','Z' vs 'Red','Green','Blue'). This means that you can basically plug colors into vector inputs and vectors into color inputs. This also means that you can use some color nodes to do operations on vectors, like in your example the color multiply node.